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                                <header>
                                        <h1 class="title">Module <code>simple_sudoku_solver</code></h1>
                                </header>
                                <section id="section-intro">
                                        <p>This module is a simple sudoku solver that will return all possible solutions
                                        for the grid.</p>
                                        <p><strong>External modules</strong>: <code>numpy</code></p>
                                        <p><code>Compatible with Python3.7 or higher</code></p>
                                        <p><em>Repository:</em> <a href="https://github.com/rickfernandes/sudoku_solver">https://github.com/rickfernandes/sudoku_solver</a></p>
                                        <details class="source">
                                        <summary>
                                        <span>Expand source code</span>
                                        </summary>
                                        <pre><code class="python"># -*- coding: utf-8 -*-
                                                &#34;&#34;&#34;
                                                This module is a simple sudoku solver that will return all possible solutions
                                                for the grid.
                                                __External modules__: `numpy`
                                                `Compatible with Python3.7 or higher`\n
                                                _Repository:_ https://github.com/rickfernandes/sudoku_solver
                                                &#34;&#34;&#34;
                                                from numpy import matrix
                                                grid = [[5,3,0,0,7,0,0,0,0],
                                                                [6,0,0,1,9,5,0,0,0],
                                                                [0,9,8,0,0,0,0,6,0],
                                                                [8,0,0,0,6,0,0,0,3],
                                                                [4,0,0,8,0,3,0,0,1],
                                                                [7,0,0,0,2,0,0,0,6],
                                                                [0,6,0,0,0,0,2,8,0],
                                                                [0,0,0,4,1,9,0,0,5],
                                                                [0,0,0,0,8,0,0,7,9]]
                                                &#34;&#34;&#34;valid sudoku grid that will be used by `solve()`&#34;&#34;&#34;
                                                solution = 1
                                                &#34;&#34;&#34;varible used to keep track of the number of solutions&#34;&#34;&#34;
                                                def possible(y,x,n):
                                                        &#34;&#34;&#34;Function to determine if a number can be inserted in a certain position
                                                        of the `grid`
                                                        Args:
                                                                `y` (int): `grid` row.
                                                                `x` (int): `grid` column.
                                                                `n` (int): number to be inserted in row `y` and column `x`.
                                                        Dependencies:
                                                                ___None___
                                                        Returns:
                                                                bool: can `n` be inserted. _False_ if not possible. _True_ otherwise.
                                                    &#34;&#34;&#34;
                                                        for i in range(9):
                                                                if grid[y][i] == n or grid[i][x] == n:
                                                                        return False
                                                        
                                                        x0 = (x//3)*3
                                                        y0 = (y//3)*3
                                                        for i in range(3):
                                                                for j in range(3):
                                                                        if grid[y0+i][x0+j] == n:
                                                                                return False
                                                        return True
                                                def solve():
                                                        &#34;&#34;&#34;Recursive function that prints all possible solutions for `grid`.
                                                        Args:
                                                                ___None___
                                                        Dependencies:
                                                                `solution` (int): global variable, increments by 1 with each solution. \n
                                                                `grid` (array): global variable, used to find the solutions. \n
                                                                `possible()` (function).
                                                        Returns:
                                                                ___None___
                                                    &#34;&#34;&#34;
                                                        global solution
                                                        for y in range(9):
                                                                for x in range(9):
                                                                        if grid[y][x] == 0:
                                                                                for n in range(9):
                                                                                        if possible(y,x,n+1):
                                                                                                grid[y][x] = n+1
                                                                                                solve()
                                                                                                grid[y][x] = 0
                                                                                return
                                                        print(&#39;-------------&#39;)
                                                        print(f&#39;Solution {solution}&#39;)
                                                        print(matrix(grid))
                                                        solution +=1
                                                def main():
                                                        &#39;Prints the original grid and calls `solve()`&#39;
                                                        print(matrix(grid))
                                                        solve()
                                                if __name__ == &#39;__main__&#39;:
                                        main()</code></pre>
                                        </details>
                                </section>
                                <section>
                                </section>
                                <section>
                                        <h2 class="section-title" id="header-variables">Global variables</h2>
                                        <dl>
                                                <dt id="simple_sudoku_solver.grid"><code class="name">var <span class="ident">grid</span></code></dt>
                                                <dd>
                                                <div class="desc"><p>valid sudoku grid that will be used by <code><a title="simple_sudoku_solver.solve" href="#simple_sudoku_solver.solve">solve()</a></code></p></div>
                                                </dd>
                                                <dt id="simple_sudoku_solver.solution"><code class="name">var <span class="ident">solution</span></code></dt>
                                                <dd>
                                                <div class="desc"><p>varible used to keep track of the number of solutions</p></div>
                                                </dd>
                                        </dl>
                                </section>
                                <section>
                                        <h2 class="section-title" id="header-functions">Functions</h2>
                                        <dl>
                                                <dt id="simple_sudoku_solver.main"><code class="name flex">
                                                <span>def <span class="ident">main</span></span>(<span>)</span>
                                                </code></dt>
                                                <dd>
                                                <div class="desc"><p>Prints the original grid and calls <code><a title="simple_sudoku_solver.solve" href="#simple_sudoku_solver.solve">solve()</a></code></p></div>
                                                <details class="source">
                                                <summary>
                                                <span>Expand source code</span>
                                                </summary>
                                                <pre><code class="python">def main():
                                                                &#39;Prints the original grid and calls `solve()`&#39;
                                                                print(matrix(grid))
                                                solve()</code></pre>
                                                </details>
                                                </dd>
                                                <dt id="simple_sudoku_solver.possible"><code class="name flex">
                                                <span>def <span class="ident">possible</span></span>(<span>y, x, n)</span>
                                                </code></dt>
                                                <dd>
                                                <div class="desc"><p>Function to determine if a number can be inserted in a certain position
                                                        of the <code><a title="simple_sudoku_solver.grid" href="#simple_sudoku_solver.grid">grid</a></code></p>
                                                        <h2 id="args">Args</h2>
                                                        <p><code>y</code> (int): <code><a title="simple_sudoku_solver.grid" href="#simple_sudoku_solver.grid">grid</a></code> row.
                                                        <code>x</code> (int): <code><a title="simple_sudoku_solver.grid" href="#simple_sudoku_solver.grid">grid</a></code> column.
                                                <code>n</code> (int): number to be inserted in row <code>y</code> and column <code>x</code>.</p>
                                                <h2 id="dependencies">Dependencies</h2>
                                                <p><strong><em>None</em></strong></p>
                                                <h2 id="returns">Returns</h2>
                                                <dl>
                                                        <dt><code>bool</code></dt>
                                                        <dd>can <code>n</code> be inserted. <em>False</em> if not possible. <em>True</em> otherwise.</dd>
                                                </dl></div>
                                                <details class="source">
                                                <summary>
                                                <span>Expand source code</span>
                                                </summary>
                                                <pre><code class="python">def possible(y,x,n):
                                                                &#34;&#34;&#34;Function to determine if a number can be inserted in a certain position
                                                                of the `grid`
                                                                Args:
                                                                        `y` (int): `grid` row.
                                                                        `x` (int): `grid` column.
                                                                        `n` (int): number to be inserted in row `y` and column `x`.
                                                                Dependencies:
                                                                        ___None___
                                                                Returns:
                                                                        bool: can `n` be inserted. _False_ if not possible. _True_ otherwise.
                                                            &#34;&#34;&#34;
                                                                for i in range(9):
                                                                        if grid[y][i] == n or grid[i][x] == n:
                                                                                return False
                                                                
                                                                x0 = (x//3)*3
                                                                y0 = (y//3)*3
                                                                for i in range(3):
                                                                        for j in range(3):
                                                                                if grid[y0+i][x0+j] == n:
                                                                                        return False
                                                return True</code></pre>
                                                </details>
                                                </dd>
                                                <dt id="simple_sudoku_solver.solve"><code class="name flex">
                                                <span>def <span class="ident">solve</span></span>(<span>)</span>
                                                </code></dt>
                                                <dd>
                                                <div class="desc"><p>Recursive function that prints all possible solutions for <code><a title="simple_sudoku_solver.grid" href="#simple_sudoku_solver.grid">grid</a></code>.</p>
                                                <h2 id="args">Args</h2>
                                                <p><strong><em>None</em></strong></p>
                                                <h2 id="dependencies">Dependencies</h2>
                                                <p><code><a title="simple_sudoku_solver.solution" href="#simple_sudoku_solver.solution">solution</a></code> (int): global variable, increments by 1 with each solution. </p>
                                                <p><code><a title="simple_sudoku_solver.grid" href="#simple_sudoku_solver.grid">grid</a></code> (array): global variable, used to find the solutions. </p>
                                                <p><code><a title="simple_sudoku_solver.possible" href="#simple_sudoku_solver.possible">possible()</a></code> (function).</p>
                                                <h2 id="returns">Returns</h2>
                                                <p><strong><em>None</em></strong></p></div>
                                                <details class="source">
                                                <summary>
                                                <span>Expand source code</span>
                                                </summary>
                                                <pre><code class="python">def solve():
                                                                &#34;&#34;&#34;Recursive function that prints all possible solutions for `grid`.
                                                                Args:
                                                                        ___None___
                                                                Dependencies:
                                                                        `solution` (int): global variable, increments by 1 with each solution. \n
                                                                        `grid` (array): global variable, used to find the solutions. \n
                                                                        `possible()` (function).
                                                                Returns:
                                                                        ___None___
                                                            &#34;&#34;&#34;
                                                                global solution
                                                                for y in range(9):
                                                                        for x in range(9):
                                                                                if grid[y][x] == 0:
                                                                                        for n in range(9):
                                                                                                if possible(y,x,n+1):
                                                                                                        grid[y][x] = n+1
                                                                                                        solve()
                                                                                                        grid[y][x] = 0
                                                                                        return
                                                                print(&#39;-------------&#39;)
                                                                print(f&#39;Solution {solution}&#39;)
                                                                print(matrix(grid))
                                                solution +=1</code></pre>
                                                </details>
                                                </dd>
                                        </dl>
                                </section>
                                <section>
                                </section>
                        </article>
                        <nav id="sidebar">
                                <h1>Index</h1>
                                <div class="toc">
                                <ul></ul>
                        </div>
                        <ul id="index">
                                <li><h3><a href="#header-variables">Global variables</a></h3>
                                <ul class="">
                                        <li><code><a title="simple_sudoku_solver.grid" href="#simple_sudoku_solver.grid">grid</a></code></li>
                                        <li><code><a title="simple_sudoku_solver.solution" href="#simple_sudoku_solver.solution">solution</a></code></li>
                                </ul>
                        </li>
                        <li><h3><a href="#header-functions">Functions</a></h3>
                        <ul class="">
                                <li><code><a title="simple_sudoku_solver.main" href="#simple_sudoku_solver.main">main</a></code></li>
                                <li><code><a title="simple_sudoku_solver.possible" href="#simple_sudoku_solver.possible">possible</a></code></li>
                                <li><code><a title="simple_sudoku_solver.solve" href="#simple_sudoku_solver.solve">solve</a></code></li>
                        </ul>
                </li>
        </ul>
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